Extent,multiplying, and proportionality rules in children's judgments of area

The study examined children's use of multiplying and proportionality rules in judgments of area. In two experiments children judged the area of rectangles. Seven-year-olds used linear extent as an index of area. Eight- and nine-year-olds replaced the extent rule with the height × width rule. In a third experiment 8-through 11-year-olds were presented with a rectangle and a horizontal line representing the width of a second rectangle. Children were asked to indicate the height that would make the second rectangle equal in area to the first. The correct response was proportional to the product of the ratio of the widths of the two rectangles and the height of the first rectangle. Graphical and statistical analyses indicated that children applied the ratio rule to these judgments. The implications for Piaget's theory of cognitive development were discussed.